Related papers: Quantum Steering Ellipsoid Volume as a Measure on …

We reexamine a recent analysis in which, using the volume of the associated quantum steering ellipsoid (QES) as a measure, we sought to estimate the probability that a two-qubit state is separable. In the estimation process, we, in effect,…

The quantum steering ellipsoid of a two-qubit state is the set of Bloch vectors that Bob can collapse Alice's qubit to, considering all possible measurements on his qubit. We provide an elementary construction of the ellipsoid for arbitrary…

While the exact separability probability of 8/33 for two-qubit states under the Hilbert-Schmidt measure has been reported by Huong and Khoi [\href{https://doi.org/10.1088/1751-8121/ad8493}{J.Phys.A:Math.Theor.{\bf57}, 445304(2024)}],…

We identify the families of states that maximise some recently proposed quantifiers of Einstein-Podolsky-Rosen (EPR) steering and the volume of the Quantum Steering Ellipsoid (QSE). The optimal measurements which maximise genuine EPR…

We conduct a pair of quasirandom estimations of the separability probabilities with respect to ten measures on the 15-dimensional convex set of two-qubit states, using its Euler-angle parameterization. The measures include the…

In a previous study (quant-ph/9911058), several remarkably simple exact results were found, in certain specialized m-dimensional scenarios (m<5), for the a priori probability that a pair of qubits is unentangled/separable. The measure used…

In previous studies, we have explored the ansatz that the volume elements of the Bures metrics over quantum systems might serve as prior distributions, in analogy to the (classical) Bayesian role of the volume elements ("Jeffreys' priors")…

In a number of previous studies, we have investigated the use of the volume element of the Bures (minimal monotone) metric -- identically, one-fourth of the statistical distinguishability (SD) metric -- as a natural measure over the…

The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid---called the quantum steering ellipsoid---in the Bloch ball. This ellipsoid provides a simple visual characterisation…

Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041)…

Substantial progress has recently been reported in the determination of the Hilbert-Schmidt (HS) separability probabilities for two-qubit and qubit-qutrit (real, complex and quaternionic) systems. An important theoretical concept employed…

We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…

We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability…

We obtain two sided estimates for the Bures volume of an arbitrary subset of the set of $N\times N$ density matrices, in terms of the Hilbert-Schmidt volume of that subset. For general subsets, our results are essentially optimal (for large…

We propose a method to verify quantum steering for two qubit states with an arbitrary amount of null results when both the steering and steered parties cannot be trusted. We converted the steering inequality proposed in a recent article…

We employ a quasirandom methodology, recently developed by Martin Roberts, to estimate the separability probabilities, with respect to the Bures (minimal monotone/statistical distinguishability) measure, of generic two-qubit and two-rebit…

The quantum steering ellipsoid (QSE) provides a geometric representation, within the Bloch picture, of all possible states to which one qubit can be steered through measurements performed on another correlated qubit. However, in most…

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled…

We pursue a number of analytical directions, motivated to some extent initially by the possibility of developing a methodology for formally proving or disproving a certain conjecture of quantum-theoretical relevance (quant-ph/0308037). It…

Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the…